Charge transport in amorphous Hf Zr O 0.5 0.5 2 D. R. Islamov,1,2,a) T. V. Perevalov,1,2 V. A. Gritsenko,1,2,b) C. H. Cheng,3 and A. Chin4,c) 1)Rzhanov Institute of Semiconductor Physics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation 2)Novosibirsk State University, Novosibirsk, 630090, Russian Federation 3)Dept. of Mechatronic Engineering, National Taiwan Normal University, Taipei, 106, Taiwan ROC 4)National Chiao Tung University, Hsinchu, 300, Taiwan ROC (Dated: March 5, 2015) 5 1 In this study, we demonstrated experimentally and theoretically that the charge transport mechanism in 0 amorphousHf Zr O isphonon-assistedtunnelingbetweentrapslikeinHfO andZrO . Thethermaltrap 2 0.5 0.5 2 2 2 energy of 1.25eV and optical trap energy of 2.5eV in Hf Zr O were determined based on comparison of 0.5 0.5 2 r experimental data on transport with different theories of charge transfer in dielectrics. A hypothesis that a M oxygen vacancies are responsible for the charge transport in Hf0.5Zr0.5O2 was discussed. 4 PACS numbers: 77.55.df, 77.84. s,72.20. i, 72.20.Jv − − Keywords: charge transport, Hf Zr O , traps, phonon-assisted tunneling 0.5 0.5 2 ] i c s Knowledge about charge transport of high-κ di- trl- eicles.ctrPicrsevisiouvsertyrainmsppoorrttansttudfoiersmwoedreernbasmedicroonelebcitnraorny- A)10-6 (a) n-Si/Hf0.5Zr0.5O2/Ni (b) 2755CC m compound like HfO2 and ZrO21–3. It was shown, ent (10-7 112755CC at. pthhaotnocnh-aarsgseisttreadntsupnonrtelminegchbaetnwisemenintraHpfsO2,24.aTndheZcrhOa2rgies ge curr10-8 m transport mechanism of ternary high-κ solid solution a k a - Hf0.5Zr0.5O2 still remains unknown. Le10-9 d In this letter, we investigate the charge transport n mechanismin Hf Zr O by comparisonof experimen- -10 o 0.5 0.5 2 10 [c tealelcdtraitcas.with different theories of charge transfer in di- A)10-6 (c) (d) Transport measurements were performed for struc- nt ( -7 2 e10 v tures Si/Hf0.5Zr0.5O2/Ni. To fabricate these structures, urr 70 wtioendfieplmossitoend nth-ean2d0-npm-ty-tpheicSkiH(1f00.50Z)r0w.5aOfe2rssoblyidpshoylsui-- kage c10-8 a 3 cal vapor deposition (PVD). Pure HfO2 and ZrO2 tar- Le -9 2 gets were bombarded by electron beams in high vacuum 10 0 chamber,andHf Zr Oweredepositedonthewaferform- 01. iWnge Hdifd0.5nZort0.a5pOp2lxyfialmnyys.pAostZ-dr/eHpofsritaitoino aonfn≃ea1linwgatsoupserod-. 10-10 1 2 3 4 1 2 3 4 5 duce the most non-stoichiometric films. The structural Applied voltage (V) Applied voltage (V) 1 properties of grown high-κ Hf Zr O dielectric were : 0.5 0.5 2 v examined by grazing incidence x-ray diffraction diffrac- Figure 1. Experimental (characters) and simulations (solid i togram (GI-XRD). The structural analysis showed that X the resulting Hf Zr O films were amorphous. All lines) current-voltage characteristics in n-Si/Hf0.5Zr0.5O2/Ni 0.5 0.5 2 structures at different temperatures. (a) Frenkel model (2), ar samples for transportmeasurements were equipped with (b) Hill model of overlapped traps (3), (c) multiphonon trap round 50-nm-thick Ni gates with a radius of 70µm. The ionization (4), (d) phonon-assisted tunneling between traps measurements were performed using a Hewlett Packard (5). 4155BsemiconductorparameteranalyzerandanAgilent E4980Aprecision LCR meter. Optical (dynamic) permittivity ε of Hf Zr O theory using the ab initio simulation code Quantum 0.5 0.5 2 was calculated in the framework of ∞density functional ESPRESSO5. Electronicstructuresanddielectricprop- erties of monoclinic Hf Zr O using 12-atom cell was 0.5 0.5 2 simulated. The structure was obtained by replacement ofa half hafnium atomto zirconiuminmonoclinic prim- a)Electronicmail: [email protected] itive cell of HfO2 with following relaxation. The similar b)Electronicmail: [email protected] approachwas described earlier6. c)Electronicmail: albert [email protected] Fig.1(a)showsasetofexperimentalcurrent-voltage 2 characteristics (I-V) of n-Si/Hf Zr O /Ni structures 0.5 0.5 2 measured at different temperatures T by characters in various shapes and colors. Positive applied voltage cor- responds to positive bias on the Ni contact. The leakage current through Hf Zr O grows exponentially with 0.5 0.5 2 V increasing of electric field (or applied voltage) and tem- e perature in accumulation mode (V >0). 5 2. Experiment results were analyzed by using different W=1.25 eV t models of charge transport in dielectrics: Figure 2. Configuration coordination energy diagram of trap I =eSN2/3P, (1) ionization process on negative charged trap in Hf0.5Zr0.5O2. Lowertermisfilledgroundstate,uppertermisexcitedempty state. where I is the full current through the sample, e is the elementary charge, S =π(70µm)2 is the contact square, N is the bulk trap density, and P is the probability rate trap ionization11 of charge carrier transfer between traps, which depends on the transport model. A mathematical model of well P = +∞ exp nWph Wopt−Wt cothWph known Frenkel law was introduced in 1938 for isolated n= 2kT − Wph 2kT × trap ionization7: ×InP−∞(Wsinohp(tW−(cid:16)Wpht/)2/kWTp)h Pi(Wt+nWph),(cid:17) (4) P (W)(cid:16)= eF exp(cid:17) 3√2m∗W3/2 , W βF√F e3 i 2√2m∗W −4 ~eF P =νexp − ,β = , (2) · kT F πε ε (cid:16) (cid:17) ! 0 areshowninFig.1(c)bysolidlines. HereW isphonon ∞ ph energy, W is optical energy of the trap, W is ther- opt t where ν is the frequency factor which was defined as mal trap energy, I are modified Bessel functions, m is n ∗ ν W/h, W is thermal ionization energy of the trap, the effective mass,and P (W) is probabilityof tunneling h ≃= 2π~ is the Planck constant, βF is Frenkel coeffi- trough a triangle barrieriof W height. Calculated set of cient, F = V/d is the electric field, d is the dielectric I-V-T curvesisveryclosetoexperimentaldata,obtained film thickness, k is the Boltzmann constant, ε is dy- values of fitting parameters include low trap density of namicpermittivityofthedielectricfilm,andε0is∞vacuum N = 2 1013cm−3 which corresponds to s = 370nm. permittivity (electric constant). Results of simulations This me×an distance between traps is much greater than (1)+(2)areshowninFig.1(a)bysolidlines. Onecansee, the film thickness of 20nm (Table I). Thus, it can be that Frenkel model describes the experiment data qual- concludedthatmultiphonontrapionizationdoesnotad- itatively very good. However, quantitative fitting pro- equately describe charge transfer in Hf Zr O . 0.5 0.5 2 cedure returns underestimated fitting parameter values: To get complete vision on the charge transport in theslopesofthe fittinglineswithFrenkelcoefficientgive Hf Zr O experiment data was simulated basing on 0.5 0.5 2 the dynamic permittivity ε =3.6 3.7, which is lower phonon-assisted tunneling between traps12: thanε (HfO )=4.48, ε (∞ZrO )=÷5.69, andcalculated 2 2 from t∞he first principals∞ε (Hf Zr O ) = 4.8 5.2. √2π~W W W FFouurtnhdervafiltuteisngthserecthuarrngeNtra=∞p1d0e7n0sc.5imty−0o3.f5aNn2d=W107=cm0÷.83eVat. P =m∗s2 Woptt−Wt exp(cid:18)− op2tk−T t(cid:19)× (5) − ν W/h 2 1014s−1correspondstomeandistancebe- exp p2s√m∗Wt sinh eFs , tw∼eentrap≃ss×=N 1/3 50µmthatiscomparabletoNi × − ~ 2kT − (cid:18) (cid:19) (cid:18) (cid:19) ≃ gatesize. Takingallthesefactsintoaccountonecancon- ResultsofthisprocedureareshowninFig.1(d). Theex- cludethatthereisnoquantitativeagreementbetweenex- perimentdataweredescribedquantitativelyandqualita- perimentsandFrenkelmodel,despitethatFrenkelmodel tivelywiththefollowingvaluesoffittingparameters(Ta- describes the experiment data qualitatively. ble I): N =3 1019cm 3, W =1.25eV, W =2.5eV, − t opt Simulating in terms of overlapped traps ionization × m /m =0.23(m is a free electronmass). Fig. 2 shows (Hill model)10 ∗ e e the configuration diagram of a negatively charged elec- tron trap. A vertical transition with a value of 2.5eV W e2/πε ε s esF 0 corresponds to the optical trap excitation, transitions of P =νexp − ∞ 2sinh , (3) − kT 2kT 1.25eV correspond to thermal trap energy. (cid:18) (cid:19) (cid:18) (cid:19) The same measurements and simulations were per- are in good quantitative agreement with experiments as formed for p-Si/Hf Zr O /Ni structures. Results are 0.5 0.5 2 wellasFrenkelmodel(Fig.1(b)). However,toolowvalue represented in Fig. 3. One can see that all model de- of frequency factor of ν 107s−1 was obtained. All val- scribe experimental curves qualitatively. Calculated val- ∼ uesofobtainedfillingparametersarecollectedinTableI. ues of fitting parameters are summarized in Table I. Results of simulations by the model of multiphonon Models of isolated (2) and overlapped (3) charged traps 3 10-6 (a) 25C (b) p-Si/Hf0.5Zr0.5O2/Ni 0.8 A) 75C p-Si/Hf Zr O /Ni nt (10-7 125C 0.5 0.5 2 e 175C age curr10-8 2 m)0.6 --11VV ++11VV Leak10-9 F/c -3V +3V -3V +3V ( 10-10 ce -5V +5V n 10-6 (c) (d) ita0.4 -5V +5V A) ac nt (10-7 ap urre C ge c10-8 0.2 a k a Le10-9 -10 10 0.0 -4 -3 -2 -1 -4 -3 -2 -1 -5 -4 -3 -2 -1 0 1 2 3 Applied voltage (V) Applied voltage (V) Applied voltage (V) Figure4. Experimentalcapacitance-voltagecharacteristicsin Figure 3. Experimental (characters) current-voltage charac- p-Si/Hf0.5Zr0.5O2/Ni structuresat different voltage limits. teristicsandsimulations(lines)inp-Si/Hf Zr O /Nistruc- 0.5 0.5 2 turesatdifferenttemperatures. (a)Frenkelmodel(2),(b)Hill model of overlapped traps (3), (c) multiphonon trap ioniza- mum capacity with an increase in the voltage amplitude tion (4), (d) phonon-assisted tunnelingbetween traps (5). indicates that the the surface chargeis significant. How- ever, it should be noted that the number of filled bulk traps n athrmhb . 3 1018cm 3 is much lower than m − can describe experiments with inadequate parameters totaltrapdensityofN =×3 1019cm 3. Thepossibleex- − × like for n-Si-based samples. Multiphonon ionization of planation of this difference is the Coulomb repulsion of neutral trap (4) has good agreement with experiments the charged particles with forming of Wigner-glass-like at N = 2 1013cm 3, which is equal than one got structures15 in the bulk of Hf Zr O . × − 0.5 0.5 2 for n-Si/Hf Zr O /Ni structure by the same trans- It was shown that oxygen vacancies are responsible 0.5 0.5 2 portmodel. Atthe sametime calculatedcurvesinterms for charge transport via HfO and ZrO 2,13,14. Thus, 2 2 of phonon-assisted tunneling between traps (5) are close one can expect that oxygen vacancies are responsible to experimental data with the same parameter values as for charge transport in Hf Zr O too. To confirm 0.5 0.5 2 that obtained for n-Si/Hf Zr O /Ni samples. this hypothesis experiments on photoluminescence and 0.5 0.5 2 Phonon-assistedtunneling between traps adequately quantum-chemical simulations are required. describes charge transport in Hf Zr O films on n-Si Recently, it was reported that orthorhombic crys- 0.5 0.5 2 and p-Si substrates. Taking these into account, we con- tallinephaseofhigh-κHf Zr O thinfilmscanbefer- 0.5 0.5 2 clude that the model of phonon-assisted tunneling be- roelectrics, being perspective material for application to tween traps describe charge transport in Hf Zr O ferroelectric random access memory (FeRAM)16–18. De- 0.5 0.5 2 films. Energy parameters of traps, such as the ther- spite that FeRAM has many advantages,retention char- maltrapenergyof1.25eVandthe opticaltrapenergyof acteristicsofFeRAMdevicesmuchtobedesiredbecause 2.5eV,aresimilarto thatinbinaryoxidesHfO 2,13, and of the depolarization effect19. A possible reason of the 2 ZrO 14. depolarizationeffectischargeleakageviatrapsofthedi- 2 Capacitance-voltage (C-V) measurements (Fig. 4) electric. To confirm or refute this hypothesis, transport show that increasing of voltage amplitude leads to shift propertiesofHf Zr O inamorphousandferroelectric 0.5 0.5 2 of the hysteresis to negative voltages. This phenomenon phases must be compared. might be caused by holes trapping on Hf Zr O in- To summarize, we examined the transport mecha- 0.5 0.5 2 terfaces or in the bulk of the dielectric. C-V shift al- nisms of amorphous solid solution Hf Zr O . It was 0.5 0.5 2 lows us to valuate the density of the filled hole traps as demonstrated that all charge transport models such as n athrmhb .3 1018cm 3inthebulkorn athrmhs . Frenkel model, Hill model, multiphonon trap ionization, m − m 6 1012cm 2 on×the surface states. It is not possible to andphonon-assistedtunnelingbetweentrapsdescribeex- − × separate percentage of the charge on the surface and in perimentdataformally,qualitatively,whileonlyphonon- the bulk, unusual C-V behavior of reducing the maxi- assisted tunneling between traps describes the charge 4 Model N (cm−3) s W (eV) Wt(eV) Wopt(eV) ν (s−1) ε∞ m∗/me F 1×107 50µm 0.8 — — ∼1014 3.6÷3.7 — Hill 3×1019 3.2nm 0.9÷1.0 — — ∼106÷107 5 — MPTI 2×1013 370nm — 0.8 1.6 — — 0.17 PAT 3×1019 3.2nm — 1.25 2.5 — — 0.23 Exp ∼1018÷1021 1÷10nm ∼1 ∼1 ∼1÷3 ∼1014÷1015 4.8÷5.2 Table I. Summary table of the values of the fitting parameters obtained from the simulation I-V characteristics for n- and p-Si/ZrO /Nistructuresindifferentmodels: (F)Frenkelmodel(2),(Hill)Hillmodel(Poollaw)(3),(MPTI)multiphonontrap 2 ionization (4), (PAT)phonon-assisted tunnelingbetween traps (5). Thelast column represent rangesof expected (reasonable) values (from calculation or literature) if any. transport in Hf Zr O quantitatively. 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